On operators from $\ell_{s}$ to $\ell_{p}\widehat{\otimes}\ell_{q}$ or to $\ell_{p}\widehat{\widehat{\otimes}}\ell_{q}$
Volume 121 / 2010
Colloquium Mathematicum 121 (2010), 25-33
MSC: Primary 46B28; Secondary 47L20.
DOI: 10.4064/cm121-1-3
Abstract
We show that every operator from $\ell_{s}$ to $\ell_{p}\mathbin{\widehat{\otimes}}\ell_{q}$ is compact when $1\leq p,q< s$ and that every operator from $\ell_{s}$ to $\ell_{p}\mathbin{\widehat{\widehat{\otimes}}}\ell_{q}$ is compact when $ 1/p+1/q>1+1/s. $
